Cycles in Random Bipartite Graphs

In this paper we study cycles in random bipartite graph $G(n,n,p)$. We prove that if $p\gg n^{-2/3}$, then $G(n,n,p)$ a.a.s. satisfies the following. Every subgraph $G'\subset G(n,n,p)$ with more than $(1+o(1))n^2p/2$ edges contains a cycle of length $t$ for all even $t\in[4,(1+o(1))n/30]$. Our theorem complements a previous result on bipancyclicity, and is closely related to a recent work of Lee and Samotij.Comment: 8 pages, 2 figure

Spartan Daily, November 22, 1982

Volume 79, Issue 57https://scholarworks.sjsu.edu/spartandaily/6971/thumbnail.jp

Műszaki informatikai problémákhoz kapcsolódó diszkrét matematikai modellek vizsgálata = Discrete mathematical models related to problems in informatics

Diszkrét matematikai módszerekkel strukturális és kvantitatív összefüggéseket bizonyítottunk; algoritmusokat terveztünk, komplexitásukat elemeztük. Az eredmények a gráfok és hipergráfok elméletéhez, valamint on-line ütemezéshez kapcsolódnak. Néhány kiemelés: - Pontosan leírtuk azokat a szerkezeti feltételeket, amelyeknek teljesülni kell ahhoz, hogy egy kommunikációs hálózatban és annak minden összefüggő részében legyen olyan, megadott típusú összefüggő részhálózat, ahonnan az összes többi elem közvetlenül elérhető. (A probléma két évtizeden át megoldatlan volt.) - Aszimptotikusan pontos becslést adtunk egy n-elemű alaphalmaz olyan, k-asokból álló halmazrendszereinek minimális méretére, amelyekben minden k-osztályú partícióhoz van olyan halmaz, ami az összes partíció-osztályt metszi. (Nyitott probléma volt 1973 óta, több szerző egymástól függetlenül is felvetette.) - Halmazrendszerek partícióira az eddigieknél általánosabb modellt vezettünk be, megvizsgáltuk részosztályainak hierarchikus szerkezetét és hatékony algoritmusokat adtunk. (Sok alkalmazás várható az erőforrás-allokáció területén.) - Kidolgoztunk egy módszert, amellyel lokálisan véges pozíciós játékok nyerő stratégiája megtalálható mindössze lineáris méretű memória használatával. - Félig on-line ütemezési algoritmusokat terveztünk (kétgépes feladatra, nem azonos sebességű processzorokra), amelyeknek versenyképességi aránya bizonyítottan jobb, mint ami a legjobb teljesen on-line módszerekkel elérhető. | Applying discrete mathematical methods, we proved structural and quantitative relations, designed algorithms and analyzed their complexity. The results deal with graph and hypergraph theory and on-line scheduling. Some selected ones are: - We described the exact structural conditions which have to hold in order that an intercommunication network and each of its connected parts contain a connected subnetwork of prescribed type, from which all the other nodes of the network can be reached via direct link. (This problem was open for two decades.) - We gave asymptotically tight estimates on the minimum size of set systems of k-element sets over an n-element set such that, for each k-partition of the set, the set system contains a k-set meeting all classes of the partition. (This was an open problem since 1973, raised by several authors independently.) - We introduced a new model, more general than the previous ones, for partitions of set systems. We studied the hierarchic structure of its subclasses, and designed efficient algorithms. (Many applications are expected in the area of resource allocation.) - We developed a method to learn winning strategies in locally finite positional games, which requires linear-size memory only. - We designed semi-online scheduling algorithms (for two uniform processors of unequal speed), whose competitive ratio provably beats the best possible one achievable in the purely on-line setting

Volume 7 - Issue 7 - Friday, November 5, 1971

The Rose Thorn, Rose-Hulman\u27s independent student newspaper.https://scholar.rose-hulman.edu/rosethorn/2038/thumbnail.jp

501 Baseball Books Fans Must Read before They Die

Propounding his “small ball theory” of sports literature, George Plimpton proposed that “the smaller the ball, the more formidable the literature.” Of course he had the relatively small baseball in mind, because its literature is formidable—vast and varied, instructive, often wildly entertaining, and occasionally brilliant. From this bewildering array of baseball books, Ron Kaplan has chosen 501 of the best, making it easier for fans to find just the books to suit them (or to know what they’re missing). From biography, history, fiction, and instruction to books about ballparks, business, and rules, anyone who loves to read about baseball will find in this book a companionable guide, far more fun than a reference work has any right to be

How Can The Aging US Transportation Infrastructure Support the Movement of Agricultural Commodities In the Future?

PowerPoint Presented at Background for Farm Bureau Discussion Meet Training, August 11, 2008Marketing,

Understanding fan culture : characteristics, terminology and limits

Fan Culture has largely been discussed when linked with Media Studies – be it regarding the effects of television and/or the Internet, or its historical evolution. This study proposes to investigate Fan Culture by exploring how it works and which are its defining characteristics, terminology and limits. Inevitably intertwined with Popular Culture, this dissertation will try to identify multiple fandoms and distinguish what unites them – as well as what separates them. Exploring topics like fan identification, as well as gender and violence (among others), will allow for a greater clarity on the impact of the phenomenon in both social and cultural life. Fan Culture can be thought of as a wide spectrum. This investigation wishes to better define and analyze the phenomenon and its dynamics. Understanding fans as both cultural objects and active agents in the production of culture, this dissertation will make use of a qualitative analysis of fundamental texts, as well as a secondary data analysis of three quantitative studies to further define the culture produced for and by the fans.A Cultura dos Fãs tem sido estudada sobretudo em associação aos Estudos dos Media - quer seja em relação aos efeitos da televisão e/ou da Internet, quer seja em relação à sua evolução histórica. Este trabalho propõe investigar a Cultura dos Fãs, explorando como funciona e quais são as suas características principais, respectiva terminologia e limites. Inevitavelmente entrelaçada com a Cultura Popular, esta dissertação procurará identificar múltiplos grupos de fãs e distinguir o que os une - assim como o que os separa. O estudo de temas como a identificação dos fãs, o género e a violência (entre outros) permitirá clarificar o impacto do fenómeno tanto na vida social como cultural. A Cultura dos Fãs pode ser pensada como um espectro amplo. Esta investigação visa definir e analisar mais a fundo o fenómeno e as suas dinâmicas. Fazendo uso dos fãs como objetos culturais e agentes ativos na produção da cultura, esta dissertação desenvolve uma análise qualitativa de textos fundamentais, bem como uma análise de dados secundários de três estudos quantitativos para definir melhor a cultura produzida para e pelos fãs